The soft-collinear bootstrap: N = 4 Yang-Mills amplitudes at six- and seven-loops

Journal of High Energy Physics

Volumn 2012, Issue 3, 2012, Pages

  Bourjaily, J L ^a   DiRe, A ^b   Shaikh, A ^c   Spradlin, M ^b   Volovich, A ^b  

^a HARVARD UNIVERSITY   (United States)

^b BROWN UNIVERSITY   (United States)

^c Brown University   (United States)

Author keywords

Scattering amplitudes; Supersymmetric gauge theory

Indexed keywords

EID: 84859616967     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP03(2012)032     Document Type: Article

References (68)

1. Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys. B 435 (1995) 59 [hep-ph/9409265] [INSPIRE].
2. Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [INSPIRE].
3. Z. Bern, J. Carrasco, H. Johansson and D. Kosower, Maximally supersymmetric planar Yang-Mills amplitudes at five loops, Phys. Rev. D 76 (2007) 125020 [arXiv:0705.1864] [INSPIRE].
4. E.I. Buchbinder and F. Cachazo, Two-loop amplitudes of gluons and octa-cuts in N = 4 super Yang-Mills, JHEP 11 (2005) 036 [hep-th/0506126] [INSPIRE].
5. F. Cachazo, Sharpening the leading singularity, arXiv:0803.1988 [INSPIRE].
6. F. Cachazo, M. Spradlin and A. Volovich, Leading singularities of the two-loop six-particle MHV amplitude, Phys. Rev. D 78 (2008) 105022 [arXiv:0805.4832] [INSPIRE].
7. M. Spradlin, A. Volovich and C. Wen, Three-loop leading singularities and BDS ansatz for five particles, Phys. Rev. D 78 (2008) 085025 [arXiv:0808.1054] [INSPIRE].
8. M. Spradlin, Multiloop gluon amplitudes and AdS/CFT, in the Proceedings of 9th Workshop on Non-Perturbative Quantum Chromodynamics, Paris France June 4-8 2007, pg. 05 [eConf C 0706044 (2007) 05] [INSPIRE].
9. Z. Bern and Y.-T. Huang, Basics of generalized unitarity, J. Phys. A 44 (2011) 454003 [arXiv:1103.1869] [INSPIRE].
10. Z. Bern, L.J. Dixon, J.J.M. Carrasco and H. Johansson, The six-loop four-point planar amplitude in N = 4 super-Yang-Mills theory, unpublished.
11. S. Caron-Huot, Loops and trees, JHEP 05 (2011) 080 [arXiv:1007.3224] [INSPIRE].
12. R.H. Boels, On BCFW shifts of integrands and integrals, JHEP 11 (2010) 113 [arXiv:1008.3101] [INSPIRE].
13. N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, S. Caron-Huot and J. Trnka, The all-loop integrand for scattering amplitudes in planar N = 4 SYM, JHEP 01 (2011) 041 [arXiv:1008.2958] [INSPIRE].
14. B. Eden, G.P. Korchemsky and E. Sokatchev, From correlation functions to scattering amplitudes, JHEP 12 (2011) 002 [arXiv:1007.3246] [INSPIRE].
15. L.F. Alday, B. Eden, G.P. Korchemsky, J. Maldacena and E. Sokatchev, From correlation functions to Wilson loops, JHEP 09 (2011) 123 [arXiv:1007.3243] [INSPIRE].
16. B. Eden, G.P. Korchemsky and E. Sokatchev, More on the duality correlators/amplitudes, arXiv:1009.2488 [INSPIRE].
17. B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, The super-correlator/super-amplitude duality: part I, arXiv:1103.3714 [INSPIRE].
18. B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, The super-correlator/super-amplitude duality: part II, arXiv:1103.4353 [INSPIRE].
19. B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, Hidden symmetry of four-point correlation functions and amplitudes in N = 4 SYM, arXiv:1108.3557 [INSPIRE].
20. B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N = 4 SYM, arXiv:1201.5329 [INSPIRE].
21. R. Akhoury, Mass divergences of wide angle scattering amplitudes, Phys. Rev. D 19 (1979) 1250 [INSPIRE].
22. A.H. Mueller, On the asymptotic behavior of the Sudakov form-factor, Phys. Rev. D 20 (1979) 2037 [INSPIRE].
23. J.C. Collins, Algorithm to compute corrections to the Sudakov form-factor, Phys. Rev. D 22 (1980) 1478 [INSPIRE].
24. A. Sen, Asymptotic behavior of the wide angle on-shell quark scattering amplitudes in non-Abelian gauge theories, Phys. Rev. D 28 (1983) 860 [INSPIRE].
25. G.F. Sterman, Summation of large corrections to short distance hadronic cross-sections, Nucl. Phys. B 281 (1987) 310 [INSPIRE].
26. S. Catani and L. Trentadue, Resummation of the QCD perturbative series for hard processes, Nucl. Phys. B 327 (1989) 323 [INSPIRE].
27. J.C. Collins, Sudakov form-factors, Adv. Ser. Direct. High Energy Phys. 5 (1989) 573 [hep-ph/0312336] [INSPIRE].
28. L. Magnea and G.F. Sterman, Analytic continuation of the Sudakov form-factor in QCD, Phys. Rev. D 42 (1990) 4222 [INSPIRE].
29. S. Catani and L. Trentadue, Comment on QCD exponentiation at large x, Nucl. Phys. B 353 (1991) 183 [INSPIRE].
30. - annihilation, Phys. Rev. D 46 (1992) 1980 [INSPIRE].
31. Z. Kunszt, A. Signer and Z. Trócsányi, Singular terms of helicity amplitudes at one loop in QCD and the soft limit of the cross-sections of multiparton processes, Nucl. Phys. B 420 (1994) 550 [hep-ph/9401294] [INSPIRE].
32. S. Catani, The singular behavior of QCD amplitudes at two loop order, Phys. Lett. B 427 (1998) 161 [hep-ph/9802439] [INSPIRE].
33. A. Vogt, Next-to-next-to-leading logarithmic threshold resummation for deep inelastic scattering and the Drell-Yan process, Phys. Lett. B 497 (2001) 228 [hep-ph/0010146] [INSPIRE].
34. G.F. Sterman and M.E. Tejeda-Yeomans, Multiloop amplitudes and resummation, Phys. Lett. B 552 (2003) 48 [hep-ph/0210130] [INSPIRE].
35. L.F. Alday, J.M. Henn, J. Plefka and T. Schuster, Scattering into the fifth dimension of N = 4 super Yang-Mills, JHEP 01 (2010) 077 [arXiv:0908.0684] [INSPIRE].
36. J.M. Henn, S.G. Naculich, H.J. Schnitzer and M. Spradlin, More loops and legs in Higgs-regulated N = 4 SYM amplitudes, JHEP 08 (2010) 002 [arXiv:1004.5381] [INSPIRE].
37. J.M. Henn, S.G. Naculich, H.J. Schnitzer and M. Spradlin, Higgs-regularized three-loop four-gluon amplitude in N = 4 SYM: exponentiation and Regge limits, JHEP 04 (2010) 038 [arXiv:1001.1358] [INSPIRE].
38. Z. Bern, M. Czakon, D. Kosower, R. Roiban and V. Smirnov, Two-loop iteration of five-point N = 4 super-Yang-Mills amplitudes, Phys. Rev. Lett. 97 (2006) 181601 [hep-th/0604074] [INSPIRE].
39. F. Cachazo, M. Spradlin and A. Volovich, Iterative structure within the five-particle two-loop amplitude, Phys. Rev. D 74 (2006) 045020 [hep-th/0602228] [INSPIRE].
40. Z. Bern, M. Czakon, L.J. Dixon, D.A. Kosower and V.A. Smirnov, The four-loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory, Phys. Rev. D 75 (2007) 085010 [hep-th/0610248] [INSPIRE].
41. Z. Bern et al., The two-loop six-gluon MHV amplitude in maximally supersymmetric Yang-Mills theory, Phys. Rev. D 78 (2008) 045007 [arXiv:0803.1465] [INSPIRE].
42. Z. Bern, L.J. Dixon and V.A. Smirnov, Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond, Phys. Rev. D 72 (2005) 085001 [hep-th/0505205] [INSPIRE].
43. J.M. Drummond and J.M. Henn, Simple loop integrals and amplitudes in N = 4 SYM, JHEP 05 (2011) 105 [arXiv:1008.2965] [INSPIRE].
44. N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo and J. Trnka, Local integrals for planar scattering amplitudes, arXiv:1012.6032 [INSPIRE].
45. T. Bargheer, N. Beisert, W. Galleas, F. Loebbert and T. McLoughlin, Exacting N = 4 superconformal symmetry, JHEP 11 (2009) 056 [arXiv:0905.3738] [INSPIRE].
46. J. Drummond, J. Henn, G. Korchemsky and E. Sokatchev, On planar gluon amplitudes/Wilson loops duality, Nucl. Phys. B 795 (2008) 52 [arXiv:0709.2368] [INSPIRE].
47. J. Drummond, J. Henn, G. Korchemsky and E. Sokatchev, Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes, Nucl. Phys. B 826 (2010) 337 [arXiv:0712.1223] [INSPIRE].
48. G. Korchemsky and A. Radyushkin, Loop space formalism and renormalization group for the infrared asymptotics of QCD, Phys. Lett. B 171 (1986) 459 [INSPIRE].
49. N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech. (2007) P01021 [hep-th/0610251] [INSPIRE].
50. L. Mason and D. Skinner, The complete planar S-matrix of N = 4 SYM as a Wilson loop in twistor space, JHEP 12 (2010) 018 [arXiv:1009.2225] [INSPIRE].
51. S. Caron-Huot, Notes on the scattering amplitude/Wilson loop duality, JHEP 07 (2011) 058 [arXiv:1010.1167] [INSPIRE].
52. A. Belitsky, G. Korchemsky and E. Sokatchev, Are scattering amplitudes dual to super Wilson loops?, Nucl. Phys. B 855 (2012) 333 [arXiv:1103.3008] [INSPIRE].
53. T. Adamo, M. Bullimore, L. Mason and D. Skinner, Scattering amplitudes and Wilson loops in twistor space, J. Phys. A 44 (2011) 454008 [arXiv:1104.2890] [INSPIRE].
54. A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, arXiv:0905.1473 [INSPIRE].
55. Z. Bern, J. Carrasco, L.J. Dixon, H. Johansson and R. Roiban, The complete four-loop four-point amplitude in N = 4 super-Yang-Mills theory, Phys. Rev. D 82 (2010) 125040 [arXiv:1008.3327] [INSPIRE].
56. Z. Bern, J. Carrasco, L. Dixon, H. Johansson and R. Roiban, Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes, arXiv:1201.5366 [INSPIRE].
57. M.B. Green, J.H. Schwarz and L. Brink, N = 4 Yang-Mills and N = 8 supergravity as limits of string theories, Nucl. Phys. B 198 (1982) 474 [INSPIRE].
58. C. Anastasiou, Z. Bern, L.J. Dixon and D. Kosower, Planar amplitudes in maximally supersymmetric Yang-Mills theory, Phys. Rev. Lett. 91 (2003) 251602 [hep-th/0309040] [INSPIRE].
59. J. Gluza, K. Kajda and D.A. Kosower, Towards a basis for planar two-loop integrals, Phys. Rev. D 83 (2011) 045012 [arXiv:1009.0472] [INSPIRE].
60. J. Drummond, J. Henn, V. Smirnov and E. Sokatchev, Magic identities for conformal four-point integrals, JHEP 01 (2007) 064 [hep-th/0607160] [INSPIRE].
61. G. Korchemsky, J. Drummond and E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops, Nucl. Phys. B 795 (2008) 385 [arXiv:0707.0243] [INSPIRE].
62. D. Nguyen, M. Spradlin and A. Volovich, New dual conformally invariant off-shell integrals, Phys. Rev. D 77 (2008) 025018 [arXiv:0709.4665] [INSPIRE].
63. P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279 [INSPIRE].
64. qgraf webpage, http://cfif.ist.utl.pt/-paulo/qgraf.html.
65. G. Brinkmann and B.D. McKay, Fast generation of planar graphs (expanded version), http://cs.anu.edu.au/-bdm/papers/plantri-full.pdf.
66. plantri and fullgen: programs for generation of certain types of planar graph webpage, http://cs.anu.edu.au/-bdm/plantri/.
67. F. Cachazo and D. Skinner, On the structure of scattering amplitudes in N = 4 super Yang-Mills and N = 8 supergravity, arXiv:0801.4574 [INSPIRE].
68. Z. Bern, J. Rozowsky and B. Yan, Two loop four gluon amplitudes in N = 4 super Yang-Mills, Phys. Lett. B 401 (1997) 273 [hep-ph/9702424] [INSPIRE].